If this is a serial-number activated LR just install on the new one and uninstall on the old one. There isn’t a formal activation count, or at least hasn’t been with the serial-number LR, so that is all you have to do.
If it is a CC-licensed LR+PS bundle, then when you install on the third computer, it’ll ask you to activate the other two, which you can do, then only ever log into one of the old ones, again. CC does keep track but makes it easy to transition to a new set of two computers without having to call Adobe.
Thanks so much for the quick reply. Had I used my brain, I would have realized that I just needed to install from the disc. I appreciate you help very much....
It would probably be more efficient to install the latest upgrade for what ever version of LR you are installing. LR 5.6 if you are installing LR 5, for example. The various updates are here: